Good question! I’m not entirely clear on
exactly what type of changes you are asking about,
but you are right that trenches are dynamic,
meaning they change over time.

A geologic trench is the location where an
ocean tectonic plate descends beneath a continent
or another ocean plate. Ocean plates descend into
a trench when they become denser than the mantle
rocks that are underneath the plates. This causes
them to sink. One way that trenches change is that
they move. Sometimes they “retreat” steadily and
sometimes they “jump”. I have included an
illustration that shows both of these processes.
trench
migration
Trenches “retreat” when the ocean plate that is
sinking “rolls back” like a dog’s tongue hanging
out of its mouth on a hot day. This causes the
trench and the upper plate to be “pulled” toward
the ocean (stage 2 of the trench retreat
illustration). Trenches can “jump” when a buoyant
piece of crust riding on the sinking plate moves
into the trench (stage 1 of the trench jump
illustration). Because it is buoyant (less dense
than the mantle that it is floating on), it can’t
sink and clogs the trench. This causes the ocean
plate to break and start sinking behind the
buoyant crust (stage 2 of the trench jump
illustration). These are two examples of how
geologic trenches change.

Answer 2:

Ocean trenches are subduction zones, zones where
one ocean plate is diving beneath the other. This
creates a furrow where the diving plate goes in,
and thus furrow is a trench.

The other is trenches that geologists dig in
order to look at layers of sediment.
Changes here happen due to different layers being
laid down for any number of reasons (typically
storms, floods, earthquakes, or other events).

Answer 3:

I am unsure of which changes you mean exactly, but
I can talk about a few changes that happen to
trenches. Trenches form where one plate is
subducting underneath another one. The trench
fills up with sediments which are either scraped
off from the subducting plate, sediments coming
off from the over-riding plate, or from regular
ocean sedimentation. So the trench may change as
different sediments are deposited into it.
Also, tectonic plates are always moving. Each one
moves in a direction at a different speed (we can
track this today using GPS!). The trench location
may move and change depending on the plate
movements.